Revealing the Majority Winner

[Bart Ingles]

>  Bart Ingles wrote:
> .<SNIP>
> > As I mentioned in my reply to Blake, when the actual level of support is
> > unknown, I tend to assume a lower value rather than the 'more-or-less
> > equidistant between top and bottom' value that people seem to infer from
> > the rankings.
> >
> > In other words, the middle candidate could be only marginally higher
> > than the bottom candidate, in which case it seems safer to give more
> > weight to the top rank.

David Marsay wrote:

> Interesting. I tend to take the opposite view.


Bart writes:

I wonder if this is an underlying view that differentiates IRO and
Condorcet supporters?

How about this -- suppose we allow the voters to rate candidates on a
scale, rather than just rank them.  Higher score means more highly
favored.  The same election could come out a couple of different ways (I
hope you are using a fixed font):

Rating: 100    80    60    40    20    0
----------------------------------------
45       A  B                          C
15       B                          C  A
40       C  B                          A

  -or-

45       A                          B  C
15       B  C                          A
40       C                          B  A

Neither IRO nor Condorcet can distinguish between the two cases.

I think it would be a mistake to pretend these voter preferences don't
exist, just because relative ranking doesn't measure them.  After a
(ranked) Condorcet election where voters' real preferences are like the
second example, imagine the backlash when some enterprising pollster
reports that when asked to rate the candidates on a 100-point scale,
voters gave the winner a median rating of 10, while one of the losers
had a median score of 90!  (Highest median score -- now there's a
method.  :-)

On the other hand, top example is no ringing endorsement of IRO.  Winner
(C) had a median score of 10, while loser (B) had a median of 90. 
Surprisingly (to me at least), Approval is the only widely discussed
method on this list that would have had a chance of handling both cases
equally well, at least without being heavily "repaired" by strategy.  I
would have thought that Approval depended more heavily on strategy than
other methods, I guess not when you are concerned about more than
ranking.  Then again, these examples probably couldn't be more
tailor-made for Approval.

Bart